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Chapter 1: Problem 13

$$\text { Simplify the given algebraic expressions.}$$ $$s+(3 s-4-s)$$

Short Answer

Expert verified
The simplified expression is \(3s - 4\).

Step by step solution

01

Simplify Inside the Parentheses

Begin by simplifying the expression inside the parentheses, which is \(3s - 4 - s\). Combine like terms: \(3s - s = 2s\). Thus, the expression simplifies to \(2s - 4\).
02

Combine Like Terms

Now substitute the simplified expression back into the original expression: \(s + (2s - 4)\). Remove the parentheses and combine like terms: \(s + 2s = 3s\). This transforms the expression to \(3s - 4\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Simplifying Expressions
Simplifying expressions is a crucial skill in algebra that helps make equations more manageable and easier to solve. When simplifying an algebraic expression, the goal is to rewrite it in its most concise and basic form. This often involves:
  • Eliminating any unnecessary parentheses
  • Combining similar components or like terms
  • Reducing mathematical statements to simpler forms
To begin with, identify any operations that can be combined or simplified. Focus first on expressions inside any parentheses. Look out for like terms, which are terms that have the same variables raised to the same power. Combining these can significantly simplify an expression, making further math easier to handle.
Combine Like Terms
Combining like terms is the process of adding or subtracting coefficients of terms that have identical variables and exponents. This skill helps streamline expressions and equations.
For example, in an expression like \(3s - 4 - s\), look for terms that can be combined. Here, both \(3s\) and \(-s\) involve the variable \(s\). Combine them by performing the operation indicated (subtraction, in this case), resulting in \(2s\).
  • Identify and underline like terms to help visualize what can be combined.
  • Match terms that share identical variables and powers.
  • Add or subtract the coefficients of these terms.
After combining like terms, the expression becomes simpler, such as \(2s - 4\), making it easier to manage in further calculations.
Parentheses in Algebra
Parentheses serve a significant role in algebraic expressions as they dictate the order of operations, guiding you on which calculations to perform first. When faced with parentheses, always take the following steps:
  • Simplify the expression inside the parentheses first before dealing with the rest of the equation.
  • Focus on any arithmetic operations or like terms contained within the parentheses.
  • Once simplified, remove the parentheses and proceed with the simplified expression.
Taking the expression \(s + (3s - 4 - s)\), begin by simplifying \(3s - 4 - s\) to \(2s - 4\). Replace the parenthesized section with this simplified form, leading to \(s + 2s - 4\). By eliminating the parentheses and simplifying further, expressions become easier to understand and solve.

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Most popular questions from this chapter

Find the value of each square root by use of a calculator. Each number is approximate. (a) \(\sqrt{3.625^{2}+0.614^{2}}\) (b) \(\sqrt{3.625^{2}}+\sqrt{0.614^{2}}\)

Solve the given problems. For what values of \(x\) is (a) \(x>\sqrt{x},\) (b) \(x=\sqrt{x}\), and (c) \(x<\sqrt{x} ?\)

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Solve the given problems. Refer to Appendix B for units of measurement and their symbols. The changes in the price of a stock (in dollars) for a given week were \(-0.68,+0.42,+0.06,-0.11,\) and \(+0.02 .\) What was the total change in the stock's price that week?

Perform the calculations on a calculator without rounding. Evaluate: (a) 2.2 + 3.8 \times 4.5 (b) (2.2 + 3.8) X 4.5
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